# Decorrelating Stationary Colored Gaussian Noise — Effect On The Desired Signal

So given stationary colored gaussian noise $\mathbf{n}$, I know that I can decorrelate it by first finding it's autocorrelation $R_{nn}$ and performing $R^{-\frac{1}{2}}_{nn} \mathbf{n}$.

In practice of course, I need to estimate $R_{nn}$, which I can do via averaging $\mathbf{r}_{nn}$ or by fitting it to an AR model.

So, suppose I have a good estimate $\hat{R}_{nn}$, for a finite data record of length $N$. Such that the resulting spectrum of the noise frame is white enough, according to some metric.

Now, suppose I have a signal $\mathbf{x} = \mathbf{s} + \mathbf{n}$. I want to decorrelate the noise, such that after the decorrelation, I get a signal in white noise. From what I have read, the way to do this is to also apply $R^{-\frac{1}{2}}_{nn} \mathbf{x}$.

However, won't this distort the desired signal $\mathbf{s}$? Can anyone point me to some references regarding this?

Also: How else can I decorrelate colored noise in order to get my signal embedded in white noise?

The Result would be the signal $\mathbf{s}$ filtered by the system which whitens the noise.